Index: crypto/third_party/curve25519-donna/curve25519-donna.cc |
=================================================================== |
--- crypto/third_party/curve25519-donna/curve25519-donna.cc (revision 0) |
+++ crypto/third_party/curve25519-donna/curve25519-donna.cc (revision 0) |
@@ -0,0 +1,731 @@ |
+/* Copyright 2008, Google Inc. |
+ * All rights reserved. |
+ * |
+ * Redistribution and use in source and binary forms, with or without |
+ * modification, are permitted provided that the following conditions are |
+ * met: |
+ * |
+ * * Redistributions of source code must retain the above copyright |
+ * notice, this list of conditions and the following disclaimer. |
+ * * Redistributions in binary form must reproduce the above |
+ * copyright notice, this list of conditions and the following disclaimer |
+ * in the documentation and/or other materials provided with the |
+ * distribution. |
+ * * Neither the name of Google Inc. nor the names of its |
+ * contributors may be used to endorse or promote products derived from |
+ * this software without specific prior written permission. |
+ * |
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
+ * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
+ * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
+ * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
+ * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
+ * |
+ * curve25519-donna: Curve25519 elliptic curve, public key function |
+ * |
+ * http://code.google.com/p/curve25519-donna/ |
+ * |
+ * Adam Langley <agl@imperialviolet.org> |
+ * |
+ * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to> |
+ * |
+ * More information about curve25519 can be found here |
+ * http://cr.yp.to/ecdh.html |
+ * |
+ * djb's sample implementation of curve25519 is written in a special assembly |
+ * language called qhasm and uses the floating point registers. |
+ * |
+ * This is, almost, a clean room reimplementation from the curve25519 paper. It |
+ * uses many of the tricks described therein. Only the crecip function is taken |
+ * from the sample implementation. |
+ */ |
+ |
+#include <string.h> |
+ |
+#include "crypto/third_party/curve25519-donna/curve25519-donna.h" |
+ |
+typedef uint8 u8; |
+typedef int32 s32; |
+typedef int64 limb; |
+ |
+/* Field element representation: |
+ * |
+ * Field elements are written as an array of signed, 64-bit limbs, least |
+ * significant first. The value of the field element is: |
+ * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ... |
+ * |
+ * i.e. the limbs are 26, 25, 26, 25, ... bits wide. |
+ */ |
+ |
+/* Sum two numbers: output += in */ |
+static void fsum(limb *output, const limb *in) { |
+ unsigned i; |
+ for (i = 0; i < 10; i += 2) { |
+ output[0+i] = (output[0+i] + in[0+i]); |
+ output[1+i] = (output[1+i] + in[1+i]); |
+ } |
+} |
+ |
+/* Find the difference of two numbers: output = in - output |
+ * (note the order of the arguments!) |
+ */ |
+static void fdifference(limb *output, const limb *in) { |
+ unsigned i; |
+ for (i = 0; i < 10; ++i) { |
+ output[i] = (in[i] - output[i]); |
+ } |
+} |
+ |
+/* Multiply a number by a scalar: output = in * scalar */ |
+static void fscalar_product(limb *output, const limb *in, const limb scalar) { |
+ unsigned i; |
+ for (i = 0; i < 10; ++i) { |
+ output[i] = in[i] * scalar; |
+ } |
+} |
+ |
+/* Multiply two numbers: output = in2 * in |
+ * |
+ * output must be distinct to both inputs. The inputs are reduced coefficient |
+ * form, the output is not. |
+ */ |
+static void fproduct(limb *output, const limb *in2, const limb *in) { |
+ output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]); |
+ output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) + |
+ ((limb) ((s32) in2[1])) * ((s32) in[0]); |
+ output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) + |
+ ((limb) ((s32) in2[0])) * ((s32) in[2]) + |
+ ((limb) ((s32) in2[2])) * ((s32) in[0]); |
+ output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) + |
+ ((limb) ((s32) in2[2])) * ((s32) in[1]) + |
+ ((limb) ((s32) in2[0])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[3])) * ((s32) in[0]); |
+ output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) + |
+ 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[3])) * ((s32) in[1])) + |
+ ((limb) ((s32) in2[0])) * ((s32) in[4]) + |
+ ((limb) ((s32) in2[4])) * ((s32) in[0]); |
+ output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[3])) * ((s32) in[2]) + |
+ ((limb) ((s32) in2[1])) * ((s32) in[4]) + |
+ ((limb) ((s32) in2[4])) * ((s32) in[1]) + |
+ ((limb) ((s32) in2[0])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[5])) * ((s32) in[0]); |
+ output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[1])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[5])) * ((s32) in[1])) + |
+ ((limb) ((s32) in2[2])) * ((s32) in[4]) + |
+ ((limb) ((s32) in2[4])) * ((s32) in[2]) + |
+ ((limb) ((s32) in2[0])) * ((s32) in[6]) + |
+ ((limb) ((s32) in2[6])) * ((s32) in[0]); |
+ output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) + |
+ ((limb) ((s32) in2[4])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[2])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[5])) * ((s32) in[2]) + |
+ ((limb) ((s32) in2[1])) * ((s32) in[6]) + |
+ ((limb) ((s32) in2[6])) * ((s32) in[1]) + |
+ ((limb) ((s32) in2[0])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[7])) * ((s32) in[0]); |
+ output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) + |
+ 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[5])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[1])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[7])) * ((s32) in[1])) + |
+ ((limb) ((s32) in2[2])) * ((s32) in[6]) + |
+ ((limb) ((s32) in2[6])) * ((s32) in[2]) + |
+ ((limb) ((s32) in2[0])) * ((s32) in[8]) + |
+ ((limb) ((s32) in2[8])) * ((s32) in[0]); |
+ output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[5])) * ((s32) in[4]) + |
+ ((limb) ((s32) in2[3])) * ((s32) in[6]) + |
+ ((limb) ((s32) in2[6])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[2])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[7])) * ((s32) in[2]) + |
+ ((limb) ((s32) in2[1])) * ((s32) in[8]) + |
+ ((limb) ((s32) in2[8])) * ((s32) in[1]) + |
+ ((limb) ((s32) in2[0])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[0]); |
+ output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[3])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[7])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[1])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[1])) + |
+ ((limb) ((s32) in2[4])) * ((s32) in[6]) + |
+ ((limb) ((s32) in2[6])) * ((s32) in[4]) + |
+ ((limb) ((s32) in2[2])) * ((s32) in[8]) + |
+ ((limb) ((s32) in2[8])) * ((s32) in[2]); |
+ output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) + |
+ ((limb) ((s32) in2[6])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[4])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[7])) * ((s32) in[4]) + |
+ ((limb) ((s32) in2[3])) * ((s32) in[8]) + |
+ ((limb) ((s32) in2[8])) * ((s32) in[3]) + |
+ ((limb) ((s32) in2[2])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[2]); |
+ output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) + |
+ 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[7])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[3])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[3])) + |
+ ((limb) ((s32) in2[4])) * ((s32) in[8]) + |
+ ((limb) ((s32) in2[8])) * ((s32) in[4]); |
+ output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[7])) * ((s32) in[6]) + |
+ ((limb) ((s32) in2[5])) * ((s32) in[8]) + |
+ ((limb) ((s32) in2[8])) * ((s32) in[5]) + |
+ ((limb) ((s32) in2[4])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[4]); |
+ output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[5])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[5])) + |
+ ((limb) ((s32) in2[6])) * ((s32) in[8]) + |
+ ((limb) ((s32) in2[8])) * ((s32) in[6]); |
+ output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) + |
+ ((limb) ((s32) in2[8])) * ((s32) in[7]) + |
+ ((limb) ((s32) in2[6])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[6]); |
+ output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) + |
+ 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[7])); |
+ output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) + |
+ ((limb) ((s32) in2[9])) * ((s32) in[8]); |
+ output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]); |
+} |
+ |
+/* Reduce a long form to a short form by taking the input mod 2^255 - 19. */ |
+static void freduce_degree(limb *output) { |
+ /* Each of these shifts and adds ends up multiplying the value by 19. */ |
+ output[8] += output[18] << 4; |
+ output[8] += output[18] << 1; |
+ output[8] += output[18]; |
+ output[7] += output[17] << 4; |
+ output[7] += output[17] << 1; |
+ output[7] += output[17]; |
+ output[6] += output[16] << 4; |
+ output[6] += output[16] << 1; |
+ output[6] += output[16]; |
+ output[5] += output[15] << 4; |
+ output[5] += output[15] << 1; |
+ output[5] += output[15]; |
+ output[4] += output[14] << 4; |
+ output[4] += output[14] << 1; |
+ output[4] += output[14]; |
+ output[3] += output[13] << 4; |
+ output[3] += output[13] << 1; |
+ output[3] += output[13]; |
+ output[2] += output[12] << 4; |
+ output[2] += output[12] << 1; |
+ output[2] += output[12]; |
+ output[1] += output[11] << 4; |
+ output[1] += output[11] << 1; |
+ output[1] += output[11]; |
+ output[0] += output[10] << 4; |
+ output[0] += output[10] << 1; |
+ output[0] += output[10]; |
+} |
+ |
+#if (-1 & 3) != 3 |
+#error "This code only works on a two's complement system" |
+#endif |
+ |
+/* return v / 2^26, using only shifts and adds. */ |
+static inline limb |
+div_by_2_26(const limb v) |
+{ |
+ /* High word of v; no shift needed*/ |
+ const uint32 highword = (uint32) (((uint64) v) >> 32); |
+ /* Set to all 1s if v was negative; else set to 0s. */ |
+ const int32 sign = ((int32) highword) >> 31; |
+ /* Set to 0x3ffffff if v was negative; else set to 0. */ |
+ const int32 roundoff = ((uint32) sign) >> 6; |
+ /* Should return v / (1<<26) */ |
+ return (v + roundoff) >> 26; |
+} |
+ |
+/* return v / (2^25), using only shifts and adds. */ |
+static inline limb |
+div_by_2_25(const limb v) |
+{ |
+ /* High word of v; no shift needed*/ |
+ const uint32 highword = (uint32) (((uint64) v) >> 32); |
+ /* Set to all 1s if v was negative; else set to 0s. */ |
+ const int32 sign = ((int32) highword) >> 31; |
+ /* Set to 0x1ffffff if v was negative; else set to 0. */ |
+ const int32 roundoff = ((uint32) sign) >> 7; |
+ /* Should return v / (1<<25) */ |
+ return (v + roundoff) >> 25; |
+} |
+ |
+static inline s32 |
+div_s32_by_2_25(const s32 v) |
+{ |
+ const s32 roundoff = ((uint32)(v >> 31)) >> 7; |
+ return (v + roundoff) >> 25; |
+} |
+ |
+/* Reduce all coefficients of the short form input so that |x| < 2^26. |
+ * |
+ * On entry: |output[i]| < 2^62 |
+ */ |
+static void freduce_coefficients(limb *output) { |
+ unsigned i; |
+ |
+ output[10] = 0; |
+ |
+ for (i = 0; i < 10; i += 2) { |
+ limb over = div_by_2_26(output[i]); |
+ output[i] -= over << 26; |
+ output[i+1] += over; |
+ |
+ over = div_by_2_25(output[i+1]); |
+ output[i+1] -= over << 25; |
+ output[i+2] += over; |
+ } |
+ /* Now |output[10]| < 2 ^ 38 and all other coefficients are reduced. */ |
+ output[0] += output[10] << 4; |
+ output[0] += output[10] << 1; |
+ output[0] += output[10]; |
+ |
+ output[10] = 0; |
+ |
+ /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19 * 2^38 |
+ * So |over| will be no more than 77825 */ |
+ { |
+ limb over = div_by_2_26(output[0]); |
+ output[0] -= over << 26; |
+ output[1] += over; |
+ } |
+ |
+ /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 77825 |
+ * So |over| will be no more than 1. */ |
+ { |
+ /* output[1] fits in 32 bits, so we can use div_s32_by_2_25 here. */ |
+ s32 over32 = div_s32_by_2_25((s32) output[1]); |
+ output[1] -= over32 << 25; |
+ output[2] += over32; |
+ } |
+ |
+ /* Finally, output[0,1,3..9] are reduced, and output[2] is "nearly reduced": |
+ * we have |output[2]| <= 2^26. This is good enough for all of our math, |
+ * but it will require an extra freduce_coefficients before fcontract. */ |
+} |
+ |
+/* A helpful wrapper around fproduct: output = in * in2. |
+ * |
+ * output must be distinct to both inputs. The output is reduced degree and |
+ * reduced coefficient. |
+ */ |
+static void |
+fmul(limb *output, const limb *in, const limb *in2) { |
+ limb t[19]; |
+ fproduct(t, in, in2); |
+ freduce_degree(t); |
+ freduce_coefficients(t); |
+ memcpy(output, t, sizeof(limb) * 10); |
+} |
+ |
+static void fsquare_inner(limb *output, const limb *in) { |
+ output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]); |
+ output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]); |
+ output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) + |
+ ((limb) ((s32) in[0])) * ((s32) in[2])); |
+ output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) + |
+ ((limb) ((s32) in[0])) * ((s32) in[3])); |
+ output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) + |
+ 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) + |
+ 2 * ((limb) ((s32) in[0])) * ((s32) in[4]); |
+ output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) + |
+ ((limb) ((s32) in[1])) * ((s32) in[4]) + |
+ ((limb) ((s32) in[0])) * ((s32) in[5])); |
+ output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) + |
+ ((limb) ((s32) in[2])) * ((s32) in[4]) + |
+ ((limb) ((s32) in[0])) * ((s32) in[6]) + |
+ 2 * ((limb) ((s32) in[1])) * ((s32) in[5])); |
+ output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) + |
+ ((limb) ((s32) in[2])) * ((s32) in[5]) + |
+ ((limb) ((s32) in[1])) * ((s32) in[6]) + |
+ ((limb) ((s32) in[0])) * ((s32) in[7])); |
+ output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) + |
+ 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) + |
+ ((limb) ((s32) in[0])) * ((s32) in[8]) + |
+ 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) + |
+ ((limb) ((s32) in[3])) * ((s32) in[5]))); |
+ output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) + |
+ ((limb) ((s32) in[3])) * ((s32) in[6]) + |
+ ((limb) ((s32) in[2])) * ((s32) in[7]) + |
+ ((limb) ((s32) in[1])) * ((s32) in[8]) + |
+ ((limb) ((s32) in[0])) * ((s32) in[9])); |
+ output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) + |
+ ((limb) ((s32) in[4])) * ((s32) in[6]) + |
+ ((limb) ((s32) in[2])) * ((s32) in[8]) + |
+ 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) + |
+ ((limb) ((s32) in[1])) * ((s32) in[9]))); |
+ output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) + |
+ ((limb) ((s32) in[4])) * ((s32) in[7]) + |
+ ((limb) ((s32) in[3])) * ((s32) in[8]) + |
+ ((limb) ((s32) in[2])) * ((s32) in[9])); |
+ output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) + |
+ 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) + |
+ 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) + |
+ ((limb) ((s32) in[3])) * ((s32) in[9]))); |
+ output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) + |
+ ((limb) ((s32) in[5])) * ((s32) in[8]) + |
+ ((limb) ((s32) in[4])) * ((s32) in[9])); |
+ output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) + |
+ ((limb) ((s32) in[6])) * ((s32) in[8]) + |
+ 2 * ((limb) ((s32) in[5])) * ((s32) in[9])); |
+ output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) + |
+ ((limb) ((s32) in[6])) * ((s32) in[9])); |
+ output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) + |
+ 4 * ((limb) ((s32) in[7])) * ((s32) in[9]); |
+ output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]); |
+ output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]); |
+} |
+ |
+static void |
+fsquare(limb *output, const limb *in) { |
+ limb t[19]; |
+ fsquare_inner(t, in); |
+ freduce_degree(t); |
+ freduce_coefficients(t); |
+ memcpy(output, t, sizeof(limb) * 10); |
+} |
+ |
+/* Take a little-endian, 32-byte number and expand it into polynomial form */ |
+static void |
+fexpand(limb *output, const u8 *input) { |
+#define F(n,start,shift,mask) \ |
+ output[n] = ((((limb) input[start + 0]) | \ |
+ ((limb) input[start + 1]) << 8 | \ |
+ ((limb) input[start + 2]) << 16 | \ |
+ ((limb) input[start + 3]) << 24) >> shift) & mask; |
+ F(0, 0, 0, 0x3ffffff); |
+ F(1, 3, 2, 0x1ffffff); |
+ F(2, 6, 3, 0x3ffffff); |
+ F(3, 9, 5, 0x1ffffff); |
+ F(4, 12, 6, 0x3ffffff); |
+ F(5, 16, 0, 0x1ffffff); |
+ F(6, 19, 1, 0x3ffffff); |
+ F(7, 22, 3, 0x1ffffff); |
+ F(8, 25, 4, 0x3ffffff); |
+ F(9, 28, 6, 0x1ffffff); |
+#undef F |
+} |
+ |
+#if (-32 >> 1) != -16 |
+#error "This code only works when >> does sign-extension on negative numbers" |
+#endif |
+ |
+/* Take a fully reduced polynomial form number and contract it into a |
+ * little-endian, 32-byte array |
+ */ |
+static void |
+fcontract(u8 *output, limb *input) { |
+ int i; |
+ int j; |
+ |
+ for (j = 0; j < 2; ++j) { |
+ for (i = 0; i < 9; ++i) { |
+ if ((i & 1) == 1) { |
+ /* This calculation is a time-invariant way to make input[i] positive |
+ by borrowing from the next-larger limb. |
+ */ |
+ const s32 mask = (s32)(input[i]) >> 31; |
+ const s32 carry = -(((s32)(input[i]) & mask) >> 25); |
+ input[i] = (s32)(input[i]) + (carry << 25); |
+ input[i+1] = (s32)(input[i+1]) - carry; |
+ } else { |
+ const s32 mask = (s32)(input[i]) >> 31; |
+ const s32 carry = -(((s32)(input[i]) & mask) >> 26); |
+ input[i] = (s32)(input[i]) + (carry << 26); |
+ input[i+1] = (s32)(input[i+1]) - carry; |
+ } |
+ } |
+ { |
+ const s32 mask = (s32)(input[9]) >> 31; |
+ const s32 carry = -(((s32)(input[9]) & mask) >> 25); |
+ input[9] = (s32)(input[9]) + (carry << 25); |
+ input[0] = (s32)(input[0]) - (carry * 19); |
+ } |
+ } |
+ |
+ /* The first borrow-propagation pass above ended with every limb |
+ except (possibly) input[0] non-negative. |
+ |
+ Since each input limb except input[0] is decreased by at most 1 |
+ by a borrow-propagation pass, the second borrow-propagation pass |
+ could only have wrapped around to decrease input[0] again if the |
+ first pass left input[0] negative *and* input[1] through input[9] |
+ were all zero. In that case, input[1] is now 2^25 - 1, and this |
+ last borrow-propagation step will leave input[1] non-negative. |
+ */ |
+ { |
+ const s32 mask = (s32)(input[0]) >> 31; |
+ const s32 carry = -(((s32)(input[0]) & mask) >> 26); |
+ input[0] = (s32)(input[0]) + (carry << 26); |
+ input[1] = (s32)(input[1]) - carry; |
+ } |
+ |
+ /* Both passes through the above loop, plus the last 0-to-1 step, are |
+ necessary: if input[9] is -1 and input[0] through input[8] are 0, |
+ negative values will remain in the array until the end. |
+ */ |
+ |
+ input[1] <<= 2; |
+ input[2] <<= 3; |
+ input[3] <<= 5; |
+ input[4] <<= 6; |
+ input[6] <<= 1; |
+ input[7] <<= 3; |
+ input[8] <<= 4; |
+ input[9] <<= 6; |
+#define F(i, s) \ |
+ output[s+0] |= input[i] & 0xff; \ |
+ output[s+1] = (input[i] >> 8) & 0xff; \ |
+ output[s+2] = (input[i] >> 16) & 0xff; \ |
+ output[s+3] = (input[i] >> 24) & 0xff; |
+ output[0] = 0; |
+ output[16] = 0; |
+ F(0,0); |
+ F(1,3); |
+ F(2,6); |
+ F(3,9); |
+ F(4,12); |
+ F(5,16); |
+ F(6,19); |
+ F(7,22); |
+ F(8,25); |
+ F(9,28); |
+#undef F |
+} |
+ |
+/* Input: Q, Q', Q-Q' |
+ * Output: 2Q, Q+Q' |
+ * |
+ * x2 z3: long form |
+ * x3 z3: long form |
+ * x z: short form, destroyed |
+ * xprime zprime: short form, destroyed |
+ * qmqp: short form, preserved |
+ */ |
+static void fmonty(limb *x2, limb *z2, /* output 2Q */ |
+ limb *x3, limb *z3, /* output Q + Q' */ |
+ limb *x, limb *z, /* input Q */ |
+ limb *xprime, limb *zprime, /* input Q' */ |
+ const limb *qmqp /* input Q - Q' */) { |
+ limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19], |
+ zzprime[19], zzzprime[19], xxxprime[19]; |
+ |
+ memcpy(origx, x, 10 * sizeof(limb)); |
+ fsum(x, z); |
+ fdifference(z, origx); // does x - z |
+ |
+ memcpy(origxprime, xprime, sizeof(limb) * 10); |
+ fsum(xprime, zprime); |
+ fdifference(zprime, origxprime); |
+ fproduct(xxprime, xprime, z); |
+ fproduct(zzprime, x, zprime); |
+ freduce_degree(xxprime); |
+ freduce_coefficients(xxprime); |
+ freduce_degree(zzprime); |
+ freduce_coefficients(zzprime); |
+ memcpy(origxprime, xxprime, sizeof(limb) * 10); |
+ fsum(xxprime, zzprime); |
+ fdifference(zzprime, origxprime); |
+ fsquare(xxxprime, xxprime); |
+ fsquare(zzzprime, zzprime); |
+ fproduct(zzprime, zzzprime, qmqp); |
+ freduce_degree(zzprime); |
+ freduce_coefficients(zzprime); |
+ memcpy(x3, xxxprime, sizeof(limb) * 10); |
+ memcpy(z3, zzprime, sizeof(limb) * 10); |
+ |
+ fsquare(xx, x); |
+ fsquare(zz, z); |
+ fproduct(x2, xx, zz); |
+ freduce_degree(x2); |
+ freduce_coefficients(x2); |
+ fdifference(zz, xx); // does zz = xx - zz |
+ memset(zzz + 10, 0, sizeof(limb) * 9); |
+ fscalar_product(zzz, zz, 121665); |
+ /* No need to call freduce_degree here: |
+ fscalar_product doesn't increase the degree of its input. */ |
+ freduce_coefficients(zzz); |
+ fsum(zzz, xx); |
+ fproduct(z2, zz, zzz); |
+ freduce_degree(z2); |
+ freduce_coefficients(z2); |
+} |
+ |
+/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave |
+ * them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid |
+ * side-channel attacks. |
+ * |
+ * NOTE that this function requires that 'iswap' be 1 or 0; other values give |
+ * wrong results. Also, the two limb arrays must be in reduced-coefficient, |
+ * reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped, |
+ * and all all values in a[0..9],b[0..9] must have magnitude less than |
+ * INT32_MAX. |
+ */ |
+static void |
+swap_conditional(limb a[19], limb b[19], limb iswap) { |
+ unsigned i; |
+ const s32 swap = (s32) -iswap; |
+ |
+ for (i = 0; i < 10; ++i) { |
+ const s32 x = swap & ( ((s32)a[i]) ^ ((s32)b[i]) ); |
+ a[i] = ((s32)a[i]) ^ x; |
+ b[i] = ((s32)b[i]) ^ x; |
+ } |
+} |
+ |
+/* Calculates nQ where Q is the x-coordinate of a point on the curve |
+ * |
+ * resultx/resultz: the x coordinate of the resulting curve point (short form) |
+ * n: a little endian, 32-byte number |
+ * q: a point of the curve (short form) |
+ */ |
+static void |
+cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) { |
+ limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0}; |
+ limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t; |
+ limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1}; |
+ limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h; |
+ |
+ unsigned i, j; |
+ |
+ memcpy(nqpqx, q, sizeof(limb) * 10); |
+ |
+ for (i = 0; i < 32; ++i) { |
+ u8 byte = n[31 - i]; |
+ for (j = 0; j < 8; ++j) { |
+ const limb bit = byte >> 7; |
+ |
+ swap_conditional(nqx, nqpqx, bit); |
+ swap_conditional(nqz, nqpqz, bit); |
+ fmonty(nqx2, nqz2, |
+ nqpqx2, nqpqz2, |
+ nqx, nqz, |
+ nqpqx, nqpqz, |
+ q); |
+ swap_conditional(nqx2, nqpqx2, bit); |
+ swap_conditional(nqz2, nqpqz2, bit); |
+ |
+ t = nqx; |
+ nqx = nqx2; |
+ nqx2 = t; |
+ t = nqz; |
+ nqz = nqz2; |
+ nqz2 = t; |
+ t = nqpqx; |
+ nqpqx = nqpqx2; |
+ nqpqx2 = t; |
+ t = nqpqz; |
+ nqpqz = nqpqz2; |
+ nqpqz2 = t; |
+ |
+ byte <<= 1; |
+ } |
+ } |
+ |
+ memcpy(resultx, nqx, sizeof(limb) * 10); |
+ memcpy(resultz, nqz, sizeof(limb) * 10); |
+} |
+ |
+// ----------------------------------------------------------------------------- |
+// Shamelessly copied from djb's code |
+// ----------------------------------------------------------------------------- |
+static void |
+crecip(limb *out, const limb *z) { |
+ limb z2[10]; |
+ limb z9[10]; |
+ limb z11[10]; |
+ limb z2_5_0[10]; |
+ limb z2_10_0[10]; |
+ limb z2_20_0[10]; |
+ limb z2_50_0[10]; |
+ limb z2_100_0[10]; |
+ limb t0[10]; |
+ limb t1[10]; |
+ int i; |
+ |
+ /* 2 */ fsquare(z2,z); |
+ /* 4 */ fsquare(t1,z2); |
+ /* 8 */ fsquare(t0,t1); |
+ /* 9 */ fmul(z9,t0,z); |
+ /* 11 */ fmul(z11,z9,z2); |
+ /* 22 */ fsquare(t0,z11); |
+ /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9); |
+ |
+ /* 2^6 - 2^1 */ fsquare(t0,z2_5_0); |
+ /* 2^7 - 2^2 */ fsquare(t1,t0); |
+ /* 2^8 - 2^3 */ fsquare(t0,t1); |
+ /* 2^9 - 2^4 */ fsquare(t1,t0); |
+ /* 2^10 - 2^5 */ fsquare(t0,t1); |
+ /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0); |
+ |
+ /* 2^11 - 2^1 */ fsquare(t0,z2_10_0); |
+ /* 2^12 - 2^2 */ fsquare(t1,t0); |
+ /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
+ /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0); |
+ |
+ /* 2^21 - 2^1 */ fsquare(t0,z2_20_0); |
+ /* 2^22 - 2^2 */ fsquare(t1,t0); |
+ /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
+ /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0); |
+ |
+ /* 2^41 - 2^1 */ fsquare(t1,t0); |
+ /* 2^42 - 2^2 */ fsquare(t0,t1); |
+ /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } |
+ /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0); |
+ |
+ /* 2^51 - 2^1 */ fsquare(t0,z2_50_0); |
+ /* 2^52 - 2^2 */ fsquare(t1,t0); |
+ /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
+ /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0); |
+ |
+ /* 2^101 - 2^1 */ fsquare(t1,z2_100_0); |
+ /* 2^102 - 2^2 */ fsquare(t0,t1); |
+ /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); } |
+ /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0); |
+ |
+ /* 2^201 - 2^1 */ fsquare(t0,t1); |
+ /* 2^202 - 2^2 */ fsquare(t1,t0); |
+ /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); } |
+ /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0); |
+ |
+ /* 2^251 - 2^1 */ fsquare(t1,t0); |
+ /* 2^252 - 2^2 */ fsquare(t0,t1); |
+ /* 2^253 - 2^3 */ fsquare(t1,t0); |
+ /* 2^254 - 2^4 */ fsquare(t0,t1); |
+ /* 2^255 - 2^5 */ fsquare(t1,t0); |
+ /* 2^255 - 21 */ fmul(out,t1,z11); |
+} |
+ |
+int curve25519_donna(u8 *, const u8 *, const u8 *); |
+ |
+int |
+curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) { |
+ limb bp[10], x[10], z[11], zmone[10]; |
+ uint8 e[32]; |
+ int i; |
+ |
+ for (i = 0; i < 32; ++i) e[i] = secret[i]; |
+ e[0] &= 248; |
+ e[31] &= 127; |
+ e[31] |= 64; |
+ |
+ fexpand(bp, basepoint); |
+ cmult(x, z, e, bp); |
+ crecip(zmone, z); |
+ fmul(z, x, zmone); |
+ freduce_coefficients(z); |
+ fcontract(mypublic, z); |
+ return 0; |
+} |